Theoretical+Background

Operations Theoretical Background



(Oracle Think Quest Education Foundation, n.d.)

** Big Ideas ** (Working Mother, n.d.) //According to Van De Walle,Karp and Bay-Williams (2010), there are four key ideas that underpin the topic of Mathematical Operations:// **Symbolic History + - ** **Queensland Syllabus approach to operations** // The previous Mathematics Syllabus (Queensland Studies Authority, 2004), is a guide for educators in relation to Mathematics within Queensland, in a Year 1-10 setting. //  Operations are introduced within the Number Key Learning Strand. Students are first introduced to Operations at a Level 1 Standard (Queensland Studies Authority, 2004). At this early Level, students can solve simple addition and subtraction problems and are able to recognise equal groups and sharing in regards to multiplication and division within everyday situations (Queensland Studies Authority, 2004). Students at a Level 2 standard according to the syllabus (Queensland Studies Authority, 2004), can solve all operation problems using simple computation. ** Key understandings of **
 * There is an interconnection between addition and subtraction, addition is responsible for naming the whole in terms of parts and subtraction is responsible for the missing parts.
 * There is an interconnection between multiplication and division, involving finding a missing factor in regards to a known factor and product.
 * The concept of division, which includes the counting of equal size groups and working out how many altogether.
 * Models can be used in solving all mathematical problems, regardless of the size of the numbers involved. Models can be used to predict the operation required within a mathematical problem.
 * Addition (+) and Subtraction (-) symbols first appeared in Germany during the late 1400s (Bassarear, 2008). Historical records suggest that these symbols were used to indicate sacks that were surplus or minus in weighting.
 * Italian merchants introduce the symbol for division (Bassarear, 2008).
 * During the mid 1500s Michael Stiffe was the first person to use the symbols + and - to represent operation symbols (Bassarear, 2008).
 * William Oughtred 1st used the letter x to represent multiplication in 1631 (Bassarear, 2008).



** ﻿ subtraction**

// Before teachers can begin developing the concepts, skills and strategies of subtraction the following must be considered: // "//W////hen you know the total and one part of the total and you have to find the other part".// Most importantly-Always //THINK ADDITION (Jamieson-Proctor, 2010).//
 * Teachers must ensure students have a grasp of the concepts, skills and strategies of addition to ensure they can see the inverse relationship between addition and subtraction (Jamieson-Proctor, 2010c). For example: i.e. 5-3=2 is the same as 2+3=5.
 * Teachers must ensure they have a strong understanding of the language model to ensure the correct order of teaching subtraction as well as correct use of materials (Jamieson-Proctor, 2010b).
 * Barmby, Bilsborough, Harries and Higgins (2009) discuss the importance of allowing children to use modelling via the use of concrete materials. Modelling addition and subtraction is conducted during the first of three stages, when representing addition and subtraction (Barmby et al., 2009).
 * Must understand the concept of subtraction. According to Jamieson-Proctor (2010b) the concept of subtraction can be defined as
 * 3 types of subtraction: Take away, Difference or Comparison and Missing addend (Jamieson-Proctor, 2010b).
 * 3 addition strategies: Count back for 0,1,2,3. Use halves (and Halves -1,-2). Use 10. (Jamieson-Proctor, 2010a)

Barmby, P., Bilsborough, L., Harries, T., & Higgins, S. (2009). //Primary Mathematics: Teaching for Understanding.// Maidenhead: McGraw-Hill Internation Ltd. Bassarear, T. (2008). //Mathematics for Elementary School Teachers// (4th ed.). USA: Houghton Mifflin Company.

Jamieson-Proctor, R. (2010a). EDX1280: Week 1 Lecture 1. Retrieved from http://usqstudydesk.usq.edu.au/file.php/15747/Week_1/Lecture_Audio_Week_1.mp3 Jamiseon-Proctor, R. (2010b). EDX1280: Lecture 2 Week 2. Retrieved from http://usqstudydesk.usq.edu.au/file.php/15747/Week_2/EDX1280_Week_2_audio_file.mp3?forcedownload=1 Jamieson-Proctor, R. (2010c). EDX1280 Tutorial 2 Tasks. Retrieved from http://usqstudydesk.usq.edu.au/file.php/15747/Week_2/Tutorial_Resources/Tutorial_2_Tasks.pdf Oracle Think Quest Education Foundation. (n.d.). //Mrs Subtraction// [image]. Retrieved August 11, 2010 from [] Queensland Studies Authority. (2004). //Mathematics Year 1 to 10 Syllabus.// Retrieved August 11, 2010 from [] Torline-Nordstrom, K. (n.d.). //Who took my square footage// [image]. Retrieved August 11, 2010 from []

Van De Walle, J., & Karp, K., & Bay-Williams, J. (2010) //Elementary & Middle School Mathematics Teaching Developmentally// (7th ed.). USA: Pearson Education, Inc.

Working mother. (n.d.). //Don't get burned by your lightbulb moment// [image]. Retrieved August 11, 2010 from []